At international level, Norman made 23 appearances for England, including in the 1962 World Cup. He was also a member of the England squad at the 1958 World Cup, but did not play.[5] He suffered a double fracture of tibia and fibula playing for Spurs against a Hungarian Select XI in November 1965,[6][7] which brought a premature end to his career.[5]

^"Spurs Show More Invention In Attack". The Times. 19 November 1965. p. 4. Near the end, too, came an unfortunate accident to Norman, a pure mischance, when he fell going for a heavy tackle, was taken from the field on a stretcher, and thence to hospital with a fractured leg.

^"Nation's Cup To Be Changed. Already Too Much Football". The Times. 20 November 1965. p. 4.